A Chinese character not pronounced in any of the standard tones

Chinese characters are normally pronounced in one of four standard tones (five, counting the neutral tone).

There is, however, at least one character which is commonly pronounced in a style which differs from any of those four (five) tones. I've heard it often enough in (melo-)dramatic moments in movies or TV programs. If you've seen your share of those, you might have heard it as well.

The mystery character?
唉 (formally āi)
It's a sighing sound, and is often pronounced in a slowly falling tone, typically accompanied by the exhalation of breath commonly associated with a sigh.

One of my dictionaries gives "(an interjection of regret or disgust) alas"; my feeling is that it is more frequently a sigh of regret than of disgust.

Another of my dictionaries gives the fixed phrase 唉聲嘆氣 (āishēngtànqì) to sigh with distress; to moan and groan. In a context like that, where it is not someone's actual sigh, it would be pronounced in its formal first tone.